Radiotherapy in the context of lung cancer can become less effective if lung biomechanics are not well-characterized. MRI of grid-tagged, inhaled hyperpolarized He-3 gas provides images with strong signal at the tag locations, allowing time-resolved tracking of regional lung motion that can be used to inform strategies for precision radiotherapy. The present work demonstrates rapid acquisition of high-quality 3D grid-tagged images obtained with 8-fold under-sampling and reconstructed using compressed sensing. The dramatic imaging acceleration inherent in this technique allows multiple 3D image sets to be acquired during a single breath-hold, effectively permitting 4D-MRI of lung motion during exhalation.
Radiotherapy of pathologies such as cancer can become less effective if unexpected changes in the position and orientation of a patient’s anatomical features occur during treatment. In the context of lung cancer treatment using radiotherapy, it is imperative to accurately characterize regional physiological lung deformation occurring during respiration in order to provide the most effective treatment.
MRI of grid-tagged, inhaled hyperpolarized He-3 gas provides images with strong signal at the tag locations, allowing time-resolved tracking of regional lung motion that can be used to inform strategies for precision radiotherapy1,2. The purpose of the present work is to develop and demonstrate a method for highly accelerated acquisition of 3D grid-tagged images based on compressed-sensing reconstruction of significantly under-sampled k-space data, in which the under-sampling scheme is tailored to the specific properties of the applied tag pattern.
MR imaging was performed in three healthy subjects using a 1.5T whole-body scanner (Siemens Avanto) and vest-shaped RF coil. He-3 gas was polarized to approximately 60% using a home-built system. He-3 images were acquired using a Cartesian readout with 3D isotropic voxel size of 4 mm using a balanced steady-state free precession pulse sequence. Following inhalation of a 1 L mixture of ~400 mL hyperpolarized He-3 and ~600 mL nitrogen, 3D tagging grids were created at breath-hold, by applying sinc-modulated RF-pulse trains consecutively along each of the three principal axes. Tag width and spacing were 11 mm and 24 mm, respectively, in each principal direction. Sequence parameters included: TR = 1.72 ms, TE = 0.86 ms, FOV = 288×448×176 mm, and matrix size = 72×112×44. Images of the tagged He-3 gas were collected at end-of-inhalation (EOI) and end-of-exhalation (EOE) for all subjects, and additionally at four intermediate phases between EOI and EOE for subjects being imaged using k-space under-sampling. Under-sampled images were reconstructed by finding minimal solutions of terms combining the L1 norm of the total variance and the wavelet transform, using adapted routines from the SparseMRI toolbox, as previously described3,4.
For a slice taken orthogonal to the readout direction, the image-space representation of the described tagging profile can be approximated as follows:
$$ I(y,z) = C_{1}\cdot \sqcap(\frac{y}{w_{tag,y}},\frac{z}{w_{tag,z}}) * III(\frac{y}{\triangle y_{tag}},\frac{z}{\triangle z_{tag}}) \cdot \sqcap(\frac{y}{w_{lung,y}},\frac{z}{w_{lung,z}}) $$
The k-space data can then be approximated as the
two-dimensional Fourier transform of the approximate image data, which is as
follows:
$$ \check{I}(k_{y},k_{z}) = C_{2}\cdot sinc({w_{tag,y}k_{y}},{w_{tag,z}k_{z}}) \cdot III({\triangle y_{tag}k_{y}},{\triangle z_{tag}k_{z}}) * sinc({w_{lung,y}k_{y}},{w_{lung,z}k_{z}}) $$
This expectation of where energy will be located in k-space can be used to inform the
creation of a pseudo-random under-sampling pattern. The likelihood of sampling
a given phase-encode line is given as follows:
$$ p(k_{y},k_{z}) = sinc({w_{tag,y}k_{y}},{w_{tag,z}k_{z}}) \cdot III({\triangle y_{tag}k_{y}},{\triangle z_{tag}k_{z}}) * exp(-[\frac{k_{y}^{2}}{2\sigma_{ky}^{2}}+\frac{k_{z}^{2}}{2\sigma_{kz}^{2}}]) $$
This sampling likelihood generally mirrors the shape of the rough expected distribution of energy in k-space, so that regions of higher energy will tend to be sampled preferentially over regions of lower energy. The amplitudes of the Gaussian and sinc functions are chosen such that the under-sampling factor for each 3D image is approximately 8. Fig. 1a shows the profile of the sampling likelihood with respect to Ny and Nz. Fig. 1b shows an example of a k-space under-sampling pattern generated using this sampling likelihood, which may be compared with the representative slice of fully-sampled k-space data shown in Fig. 1c.